Question

1. An individual is confronted with three commodities x, y and z. Suppose the consumer’s money income is Birr 39 and the marginal utility of each good is independent of the amount consumed of other goods. Using the hypothetical data given below, find the optimum quantities of a consumer.
Unit of each good 1 2 3 4 5 6 7 8 9 10
Mux 12 11 10 9 8 7 3 0 -2 -6
MUy 60 55 48 40 27 21 19 18 9 0
MUz 70 60 50 45 30 25 18 10 0 -5
a) If the three goods were “free” or no budget constraint.
b) If respective prices are Px= 1 Birr, Py=3 Birr and Pz=5 Birr

Answer 1

For maximizing the satisfaction power the condition should be :

$\frac{MUx}{Px}=\frac{MUy}{Py}=\frac{MUz}{Pz}$

Answer: Given income 39 , if they buy 4 units of commodity x , 5 units of commodity y and 4 units of commodity z then gain maximum satisfaction because 

$4x1=4\\5x3=15\\4x5= 20\\4+15+20 =39$